The culture secretary, Maria Miller, will tell newspaper editors and proprietors on Tuesday that she will impose full statutory controls on the industry unless it comes up with a new and effective system of self-regulation and an acceptable timetable.

Her threat is designed to persuade the newspaper industry that it has to deliver a system of independent regulation swiftly, or find the public will have lost patience.

Pressed in a Commons debate on the Leveson report by Jack Straw and Sir Malcolm Rifkind, she said "if action is not taken as requested in terms of putting together a self-regulatory approach", the government response "would include legislation".

Her warning came as two central figures, David Blunkett, the former Labour home secretary, and John Whittingdale, the Conservative culture select committee chairman, shifted ground. Both had been opposed to statutory regulation.

Blunkett told the Guardian: "Before Leveson was published, there was opposition to statutory regulation, but [Leveson] has come up with a clever wheeze of an independent self-regulator with a recognition body underpinned by statute. Well, I call that oversight and it is possible to see an oversight body independently appointed, possibly by a committee of public appointments. I don't think that oversight body should be Ofcom as Leveson suggests because that would be a regulator regulating another regulator.

"If we can get to a point where everyone is agreed on the principles that have been laid down for the independent regulator, and it is independent, that they can agree on a mechanism for getting the membership of that body in place, that they can then actually ensure we have the oversight that is necessary and people seek, I think there's a chance we might have cracked it," he said.

Equally, Whittingdale pointed out that the Irish defamation act 2009 allows the courts to take account of whether a journalist has adhered to the Irish Press Council's code. Whittingdale said this was an entirely sensible way to give press proper incentives to join a press regulator, and would allow a regulator to be recognised by statute but not set up by statute.

Both sets of remarks suggest it might yet be possible to find common ground in the increasingly muddy debate.

Repeating the mantra that the status quo is not an option, Miller said: "We will see change. That change can either come with the support of the press, or if we are given no option, without it. Be in no doubt, if the industry does not respond, we will."

The credibility of her threat is likely to be questioned since she and the prime minister have said they are opposed in principle to even a milder form of regulation whereby self-regulation would be underpinned through statute by the media regulator, Ofcom.

She said during the debate that the Leveson report marks a dark moment in the history of the British press, and revealed "despicable intrusions into peoples' lives, many of whom had suffered extensively".

Miller will meet newspaper editors in Downing Street with the prime minister attending for some of the time.

She said she will ask the industry for a timetable for action, but will stress she is not going to arbitrate if there are differences within the industry.

She will also say she will not draw up a blueprint for the industry beyond saying it should match the "Levensonian principles" of independence, access to justice and an enforceable code of conduct.

She said: "This is not about the press coming up with a model that suits its own ends. The days of a press complaints commission mark two are well and truly gone. We will not accept a puppet show with the same people pulling the same strings."

But she also warned any mild underpinning legislation could lead to more draconian legislation in the future by other parliaments.Separately, Miller held cross-party talks with Labour and the Liberal Democrats. She promised to share her thoughts on a draft bill setting out how independent regulation could be underpinned by statute. For Labour, Lord Falconer, the former lord chancellor, will present an alternative draft bill for those ongoing talks, based on the Irish model of state underpinning of media regulation, a two-clause bill.

The cross-party talks are likely to have a bill ready within two weeks, and Cameron will be aware that, as things stand, there is a majority in the Commons for an underpinning bill.

Edward Garnier, the former Conservative solicitor general, and a libel lawyer, became the latest Conservative to support statutory underpinning. He said: "We are not talking about the statutory control of the press. Can we try and move away from the hyperbole and exaggeration which seems to suggest Lord Justice Leveson is demanding some Stalinistic control of the press?"